Detecting small earthquakes using the theoretical Green's function of virtual earthquakes as templates
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摘要:
搜寻小地震而得到更加完备的地震目录是地震学的基本课题.传统的匹配滤波方法用已知地震的波形与连续观测做互相关，可有效识别小地震.然而，一些地区缺乏早期观测或地震活动性低而无真实地震可做模板，造成传统匹配滤波法难以施展.使用虚拟地震的理论波形做模板可解决该问题.若使用的虚拟地震包含所有可能的震源机制，即离散地覆盖整个震源机制解空间，虚拟地震的数量将大量增加，导致计算量剧增.本研究借鉴裁剪-粘贴法（CAP）中对滑动互相关的处理方式，发展了以虚拟地震的理论格林函数为模板的匹配滤波方法（Green's function-based matched filter，简称为GFMF），在不改变计算结果的前提下通过减少滑动互相关的次数，节省计算时间.本文将该方法应用到加州一地震序列，凭借对震源位置和震源机制的网格搜索，得到了该序列的时空分布变化特征和该区域全部中等地震的震源机制.研究结果显示，虚拟地震可以用作模板来检测小地震以解决真实模板地震不足的问题.若不对虚拟地震的震源机制进行遍历，得到的地震数量将减少70%以上.这表明本研究对震源机制遍历的相关优化是重要的.
Abstract:Detecting small earthquakes to get completer seismic catalogs is one primary topic of seismology. The traditional matched-filter method cross-correlates known earthquakes' waveforms with continuous waveforms, effectively detecting small earthquakes. However, some areas may lack early observations or have low seismic activity. Such areas cannot provide enough real earthquakes as templates, making it is challenging to implement the traditional matched-filter method. The theoretical waveform of the virtual earthquake as templates can solve the above problems. If the virtual earthquakes have varying focal mechanisms, the amount of calculation will increase significantly. We learn from the processing method of sliding cross-correlation in the CAP method and develop a Green's function-based matched filter (GFMF) method. GFMF can obtain the same results but need less computational time by optimizing the number of cross-correlation. We apply this method to a region in California and obtain the temporal evolution and spatial distribution characteristics of an earthquake sequence and all moderate earthquakes' focal mechanism in the region with grid searches of the source locations and focal mechanisms.The research results show that virtual earthquakes can be used as templates to detect small earthquakes to solve insufficient template earthquakes. The study results show the detection number will be reduced by more than 70% without the grid search of focal mechanisms, which shows that the optimization of the focal mechanism searching in this study is important.
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Key words:
- Seismic events detecting /
- Matched filter /
- Template matching /
- Green's function
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图 2
实际测试中的一天12个台站的8个虚拟震源的mean CC的振幅分布图
Figure 2.
Histograms for amplitudes values in mean CCs from 1-day real observed data of 12 seismic stations and 8 virtual-template events
图 5
一个被GFMF识别到，但未被SCSN地震目录收录的地震的波形拟合情况
Figure 5.
Waveform fitting of one example event newly detected by the GFMF method but not existing in the SCSN catalog
图 6
GFMF搜索结果和SCSN地震目录中地震事件的时间变化和空间分布，及二者震源参数的差异分布
Figure 6.
Time evolution and spatial distribution of GFMF detections and the SCSN catalog, and their difference of source parameters
图 7
震级、波形振幅和地震数量的关系
Figure 7.
Relationship between magnitude, waveform amplitudes and the number of earthquakes
图 8
Match & Locate搜索结果和SCSN地震目录中地震事件的时间变化，及二者震源参数的差异分布
Figure 8.
Time evolution of Match & Locate and the SCSN catalog, and their difference of source parameters
图 10
GFMF和Match & Locate搜索结果在发震时刻(a)和震中位置(b)的差异分布图
Figure 10.
Histograms of the difference respectively in the origin time (a) and epicenter (b) between the Match & Locate detections and SCSN catalog
图 12
地震事件20181109145809的波形拟合情况
Figure 12.
Waveform fitting of seismic event 20181109145809
图 13
完整震源机制解空间和单个震源机制解识别到的地震总数(a)和识别率(b)的对比
Figure 13.
Total detection number (a) and detection rate (b) of virtual-template events with varying and fixed focal mechanism(s)
表 1
各理论测试中不同干扰因素得到的不同的结果
Table 1.
Different result obtained by different interference factors in theoretical tests
干扰因素 输入和得到的震源参数的差异 最大平均互相关值 基本测试 无 完全一致 100.0% 震源时间函数测试 加入了底边为0.2 s的等腰三角形的震源时间函数 发震时刻延迟0.1 s 84.7% 噪声测试 在上一行的基础上，加入0.5倍的真实噪声 同上 34.0% 复杂模型测试 在上一行的基础上，改用PREM模型搜索 发震时刻提前1.5 s，震中位置和震源机制为输入值的相邻网格位置 8.06% 
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表 2
大于3级地震的GFMF搜索结果和SCSN地震目录的震源参数差异的统计值
Table 2.
Statistical values of the difference in source parameters between GFMF detections and SCSN cataloged earthquakes with magnitude greater than 3
中值 平均值 最小值 最大值 发震时刻 1.25 s 1 s 0.31 s 1.66 s 震中 1.9 km 2 km 0.1 km 3.9 km 震源深度 1.1 km 2 km 0.1 km 4.9 km P轴 12° 13° 6° 25° T轴 11° 13° 1° 29° N轴 12° 16° 5° 37°
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表 3
不同阈值的误检估计
Table 3.
False detection estimation of different thresholds
阈值(MAD倍数) 候选检测中的误检数(双精度) 候选检测总数 误检率 8 46487.4556950635 8102992 0.57% 9 869.989766776939 2313281 0.040% 10 10.4419068023844 674619 0.0015% 11 0.0802513102371449 196926 0.000041% 12 4.54252699455537×10-4 57313 0.00000079% 13 0 16555 0
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表 4
不同阈值的检测总数和识别率
Table 4.
Total number of detections and recognition rate of different thresholds
阈值(MAD倍数) 检测总数 对SCSN目录事件的识别率 8 43561 98.3% 9 14514 98.0% 10 5895 97.3% 11 3273 97.1% 12 2149 94.6% 13 1428 83.0%
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